A reproducing kernel Hilbert space method for solving integro-differential equations of fractional order
type: Item
instance of: scholarly article
title: A reproducing kernel Hilbert space method for solving integro-differential equations of fractional order
zbMATH Open document ID: 1273.65194
author: Samia Bushnaq
author: Shaher Momani
author: Yong Zhou
published in: Journal of Optimization Theory and Applications
publication date: 2013-05-08T00:00:00Z
review text: The authors, using the notion of the fractional derivative of Caputo, construct an approximate method to solve the integro-differential equation of fractional order of the special form \[ D^{\alpha}u(x)= F(x, u(x), Tu(x)),\qquad m-1<\alpha\leq m,\qquad 0\leq x\leq 1, \] with \( Tu(x)=\int^{x}_{0}h(x,t)u(t)dt.\) The solution \( u(x)\) is presented as convergent power series. The algorithm of the numerical computations is not strictly formulated.
reviewed by: Ivan Secrieru
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 46E22
zbMATH DE Number: 6161525
zbMATH Keywords: reproducing kernel Hilbert space method
zbMATH Keywords: iterative method
zbMATH Keywords: nonlinear integro-differential equations of fractional order
zbMATH Keywords: algorithm
MaRDI profile type: Publication
full work available at URL: s10957-012-0207-2
OpenAlex ID: W2015597220
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DOI: 10.1007/S10957-012-0207-2
description: scientific article; zbMATH DE number 6161525